Q102 / 180 · KCET 2016 · Mathematics
The rate of change of area of a circle with respect to its radius \( r=2 \mathrm{cms} \) is
- A\( 04 \)
- B\( 2 \pi \)
- C\( 12 \)
- Correct answerD\( 4 \pi \)
Solution
We know that, area of circle is given by
\[ A=\Pi r^{2} \]
\[ \text { So, } \frac{d A}{d r}=2 \Pi r \]
At \( r=2 \mathrm{~cm} \), we have \( \left(\frac{d A}{d r}\right)_{r=2}=4 \Pi \)
\[ A=\Pi r^{2} \]
\[ \text { So, } \frac{d A}{d r}=2 \Pi r \]
At \( r=2 \mathrm{~cm} \), we have \( \left(\frac{d A}{d r}\right)_{r=2}=4 \Pi \)
Hence, the correct answer is option: 'D'.